Over-the-Air Computation in Correlated Channels

Over-the-Air (OTA) computation is the problem of computing functions distributed data without transmitting entirety to a central point. By avoiding such costly transmissions, OTA schemes can achieve better-than-linear (depending on function, often logarithmic or even constant) scaling communication cost as number transmitters grows. Among most common computed are linear weighted sums. In this work, we propose and analyze an analog scheme for class that contains well some nonlinear $p$-norms vectors. We prove error bound guarantees valid fast-fading channels all distributions fading noise contained in sub-Gaussian distributions. This includes Gaussian distributions, but also many other practically relevant cases Class A Middleton with dominant line-of-sight components. addition, there be correlations so presented results apply to, example, block bursty interference. do not rely any stochastic characterization arguments function; particular, no assumption these drawn from identical independent probability Our analysis nonasymptotic therefore provides bounds finite channel uses. has huge potential reducing applications Machine Learning (ML)-based anomaly detection large wireless sensor networks. illustrate through extensive numerical simulations.